Download Chapter 5 Review Handout File

Geometry - Chapter 5 Review – Polygon Properties
Name ______________________________________
Date __________
Hour __________
Complete each statement by filling in the blank.
1. The sum of the measures of the n interior angles of an n-gon is ____________________.
2. For an equiangular n-gon, each interior angle can be found using the formula _____________.
3. For any polygon, the sum of the measures of a set of exterior angles is ______________.
4. The ________________ angles of a kite are congruent.
5. The diagonal connecting the vertex angles of a kite is the ______________________________ of the
other diagonal.
6. The vertex angles of a kite are _________________ by a ______________________.
7. The consecutive angles between the bases of a trapezoid are ________________________.
8. The base angles of an isosceles trapezoid are ___________________.
9. A midsegment of a triangle is parallel to the third side and ________________ the length of the
_______________________.
10. The midsegment of a trapezoid is parallel to the bases and is equal in length to the ________________
of the lengths of the ______________.
11. The opposite angles of a parallelogram are __________________.
12. The consecutive angles of a parallelogram are ___________________________.
13. The diagonals of a rhombus are _____________________ and they _______________ each other.
14. The diagonals of a rectangle are ___________________ and they _______________ each other.
15. The diagonals of a square are ______________, ____________________, and ___________ each other.
16. How many sides does a polygon have if the sum of its angle measures is 3240o?
17. How many sides does an equiangular polygon have if each interior angle measures 140o?
18. What is the measure of an exterior angle of an equiangular octagon?
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Geometry - Chapter 5 Review – Polygon Properties
19. Find each lettered angle measure using your conjectures.
a = ________
b = ________
c = ________
d = ________
e = ________
f = ________
g = ________
h = ________
20.
21.
s
s = _____
m = _____
n = _____
p = _____
r = _____
s = _____
t = _____
t =_____
22. Perimeter = 64
23.
a
x
y
24.
x = _____
y = _____
25.
x = _____
m = _____
a = _____
w = _____
x = _____
y = _____
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Geometry - Chapter 5 Review – Polygon Properties
26.
27. For the parallelogram below, find m and n.
a = _____
b = _____
x = _____
y = _____
m = _____
28.
29.
n = _____
b
c
7 cm
a
a = _____
b = _____
c = _____
d = _____
a = _____
b = _____
c = _____
30. Complete the table below by placing a yes (to mean always) or a no (to mean not always) in each empty
space.
Kite
Opposite sides
are parallel
Opposite sides
are congruent
Opposite angles
are congruent
Diagonals bisect
each other
Diagonals are
perpendicular
Diagonals are
congruent
Isosceles
Trapezoid
Parallelogram
Rhombus
Rectangle
Square
Yes
Yes
No
No
No
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Geometry - Chapter 5 Review – Polygon Properties
31. A regular pentagonal mirror frame is to be built from strips of 2-inch-wide pine lattice. At what angles a
and b should the lattice be cut?
a = __________
b = __________
32. A 2-inch-wide frame is to be built around the regular decagonal window shown. At what angles a and b
should the corners of each piece be cut?
a = __________
b = __________
33. Prove that if the opposite sides of a quadrilateral are congruent, then it is a parallelogram.
Hint: Draw KM .
Given: Quadrilateral JKLM with JM  KL and JK  ML
Show: JKLM is a parallelogram
Quadrilateral
JKLM with
JM  KL and
JK  ML
JK LM
CPCTC
Converse of
Parallel Lines Conj.
Given
Definition of
Parallelogram
Same segment
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Geometry - Chapter 5 Review – Polygon Properties
34. Prove the conjecture: The diagonals of a rhombus bisect the angles.
Given: Rhombus DENI, with diagonal DN
Show: Diagonal DN bisects D and N
Flowchart Proof
DE  ____
DENI is a
rhombus
_________
___________________
1   ______
3   ______
 ______   ______
NE  ____
_______________
________
________
DN  ____
_______________
DN bisects
IDE and
INE
__________________
A
35. Prove the Parallelogram Opposite Sides Conjecture.
Given: Parallelogram ABCD
Show: AB  CD and AD  CB
Complete the Flowchart Proof
D
2
1
>
>
4
3
B
C
AB | | CD
Definition of
parallelogram
________________
Parallelogram
ABCD
given
_________________
_____________
______________
_________________
_______________
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